By H. Behrens, J. Jänecke (auth.), H. Schopper (eds.)
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Additional info for Numerical Tables for Beta-Decay and Electron Capture
Decay functions in table III. Inside the nucleus we have neglected the exchange terms. Outside the nucleus the additional exchange interaction terms needed in the potential are included in the approximation of SLATER [%J: V ezch = Cel’s, with e = number of electrons per unit of volume (in natural units), C = (81/84”3 - a. * The parameterVe needed in the Rose-WKB screening formula [S, 9, IO] is the potential energy shit at the surface of the nucleus due to the atomic electrons. For the potential outside the nucleus V(r)=-$$qe-b,r i used to calculate the screenedfunctions (see description of table III) Ve has the form Vo~rtZ&ibi.
The parameterVe needed in the Rose-WKB screening formula [S, 9, IO] is the potential energy shit at the surface of the nucleus due to the atomic electrons. For the potential outside the nucleus V(r)=-$$qe-b,r i used to calculate the screenedfunctions (see description of table III) Ve has the form Vo~rtZ&ibi. i The ratios of screened to unscreened Fob calculated with the Rose-WKB-formula and the above values for Vc arc for higher electron momenta in excellent agreement with the exact ratios from table III.
The constants ai and b( which appear in the expression for the potentials outside the nucleus are taken from the papers of TIETZ and STRAND[51,52] for 2 2 36 and of BONHAM and STRAND for Z > 36. These constants were determined by fitting the above equation to Hartree-Fock potentials for Z 5 36 and to Thomas-Fermi-Dirac potentials for Z > 36 by the method of least squares. Due to the extensive computer time required for this tabulation, the ratios of the screened to the unscreened functions are listed for a much smaller number of momentum values than for the unscreened functions in table II.
Numerical Tables for Beta-Decay and Electron Capture by H. Behrens, J. Jänecke (auth.), H. Schopper (eds.)